Numerical modelling of ice shelf dynamics

Abstract

By considering the basic stress equations for a unit volume of ice, a set of differential equations describing ice shelf flow is derived. In view of the lack of basal shear stresses at the bottom of ice shelf a model simulation which is restricted to the horizontal dimensions will not imply substantial errors. The model is applied to the Filchner-Ronne Ice Shelf, Antarctica, and model equations are solved in terms of finite differences on a 10 × 10 km grid. Present ice thickness data and boundary conditions, i.e. the balance velocities at the grounding line and strain rates at the ice front are entered as input. Using a non-linear Glen-type flow law (n=3) and a constant depth-averaged flow law parameter, representing an ice temperature of −17°C, a convincing velocity field is derived as a solution of the model equations. The model takes into account restrained flow across ice rumples where sufficient field data are available. A diagnostic run reproducing present velocity magnitudes is followed by two prognostic runs, each representing 2000 years of simulation. Transient ice thickness changes are obtained from solving the mass conservation equation. Two different assumptions concerning basal melting rates demonstrate its importance to ice shelf dynamics. Assumptions are: a) no basal melting, b) basal melting rates (−2m a⁻¹ to +3m a⁻¹) as derived from model results and geophysical field data.